I assume we are not talking about a radio thing here right, I ask this since you posted in "Audio & Electronics". My ECT button is located on the center console just below the vents. When I hit mine, a green light on the dash reads "ECT PWR". If we are talking about the same thing, then there should be a light on the dash.
The ECT button raises the shift point of each gear on the transmission. The transmission shifts at a higher RPM compared to the regular mode. It is suppose to give you more power and is good for things like towing, driving in the mountians and just general 'hot dogging it'. In general your gas mileage should be slightly lower.
If you light pops up in the dash and then goes away each time you hit it, that is not normal. It should stay on when it is on and stay off when it is off. I bet the ECT still works, now the question is "When do you have ECT on and when do you have it off?".
I would go to a flat road and accelerate at a steady pace and notice were the transmission shifts, (at what RPM), then stop and hit the button and try it again. Hopefully the shift points will be different.
If it is no difference I would get the system fixed and if the shift points are different I would get that light fixed.